Mathematics

General Solution

The general solution to a system of linear equations AX = b describes all possible solutions. You can find the general solution by:

1. Solving the corresponding homogeneous system AX = 0. Do this using the null command, by typing null(A). This returns a basis for the solution space to AX = 0. Any solution is a linear combination of basis vectors.
2. Finding a particular solution to the non-homogeneous system AX = b.

You can then write any solution to AX = b as the sum of the particular solution to AX = b, from step 2, plus a linear combination of the basis vectors from step 1.

The rest of this section describes how to use MATLAB to find a particular solution to AX = b, as in step 2.

Computational Considerations

Square Systems